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Quantum Interference & Entanglement

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Quantum Interference & Entanglement QIE - Quantum Interference & Entanglement Physics 111B: Advanced Experimentation Laboratory University of California, Berkeley Contents 1 Quantum Interference & Entanglement Description (QIE)2 2 Quantum Interference & Entanglement Pictures2 3 Before the 1st Day of Lab2 4 Objectives 3 5 Introduction 3 5.1 Bell's Theorem and the CHSH Inequality ............................. 3 6 Experimental Setup 4 6.1 Overview ............................................... 4 6.2 Diode Laser.............................................. 4 6.3 BBOs ................................................. 6 6.4 Detection ............................................... 7 6.5 Coincidence Counting ........................................ 8 6.6 Proper Start-up Procedure ..................................... 9 7 Alignment 9 7.1 Violet Beam Path .......................................... 9 7.2 Infrared Beam Path ......................................... 10 7.3 Detection Arm Angle......................................... 12 7.4 Inserting the polarization analyzing elements ........................... 12 8 Producing a Bell State 13 8.1 Mid-Lab Questions.......................................... 13 8.2 Quantifying your Bell State..................................... 14 9 Violating Bell's Inequality 15 9.1 Using the LabVIEW Program.................................... 15 9.1.1 Count Rate Indicators.................................... 15 9.1.2 Status Indicators....................................... 16 9.1.3 General Settings ....................................... 16 9.1.4 Snapshots........................................... 16 10 After the Experiment 17 11 Extensions 17 11.1 Double slit quantum eraser ..................................... 17 12 Trouble shooting 18 References 19 1 1 Quantum Interference & Entanglement Description (QIE) • Pre-requisites: Physics 137A • Days Allotted for the Experiment: 6 Attention: There is NO eating or drinking in the 111-Lab anywhere, except in rooms 282 & 286 LeConte on the bench with the BLUE stripe around it. Thank You, the Staff. This lab will be graded 30% on theory, 40% on technique, and 30% on analysis. For more information, see the Advanced Lab Syllabus. Comments: Submit feedback using this form. 2 Quantum Interference & Entanglement Pictures Figure 1: Quantum Figure 2: Inside the optics box Figure 3: Outside the Interference & Click here to see larger picture optics box Entanglement Experiment Click here to see larger Click here to see larger picture picture 3 Before the 1st Day of Lab Complete the QIE Pre Lab found in the Signature Sheet for this lab. Print the signature sheet, discuss the experiment and pre-lab questions and answers with any faculty member or GSI, and receive their signature. In the course of the lab there will be examination points where you must STOP and get a GSI or professor to verify your understanding and/or verify proper experimental setup. You cannot skip these checkpoints, and must receive signatures demonstrating that you've consulted the staff. Some experiments may have mid lab questions that must be completed by specific days of the experiment. The completed Signature Sheet MUST be submitted as the first page of your lab report. Quick links to the checkpoint questions are found here: 12345 1. View the introduction video or this experiment. Read the references [1], [2], [3], [4], [5], [6] below. [1] and [5] are particularly useful. 2 2. Read the Optics Tutorial, in particular sections 1.41 (Polarization), 1.46 (Waveplates, and 1.55 (Beamsplitter Cubes). You should also look at Optical Coatings (all of our waveplates have antireflec- tion coatings), and Intro to Laser Technology. You will not get very far if you do not understand how these optics work, it will be essential to prepare before you start working on the lab. 3. Complete the training for the safe use of lasers detailed on the Laser Safety Training page. This includes readings, watching a video, taking a quiz, and filling out a form. 4. Last day of the experiment please fill out the MOT Experiment Evaluation You should keep a laboratory notebook. The notebook should contain a detailed record of everything that was done and how/why it was done, as well as all of the data and analysis, also with plenty of how/why entries. This will aid you when you write your report. Other References [Physics 111 Library Site] 4 Objectives • Learn and experience quantum mechanics and in particular entanglement • Learn to handle and align optics (Half-Wave plates, Polarized Beam Splitters, etc...) • Learn about coincidence techniques • Learn how to violate Bell's Inequality 5 Introduction This experiment tests the validity of quantum mechanics against local hidden variable theories in describing entanglement phenomena. It takes the form of a quantum optics experiment using polarization-entangled photon pairs. 5.1 Bell's Theorem and the CHSH Inequality John Bell showed that any theory in which properties are local and are well-defined prior to measurement must obey certain limitations. Interestingly, quantum mechanics exceeds those limits set by these so-called Bell-inequalities. Therefore, observing that nature does exceed these limits makes a good case for quantum mechanics and proves that there exists no local realistic theory that can describe nature accurately. One particular version of the Bell's theorem is the so-called CHSH inequality (named after Clauser, Horne, Shimony, and Holt). To make the discussion more concrete, we will assume a photon source that sends two photons one to each of two distant locations. The degree-of-freedom we will study is the polarization of these photons. We will be interested only in events where the polarization of both photons has been detected successfully. First let us define the parity of the polarization correlations: N − N − N + N N − N − N + N E = vv vh hv hh = vv vh hv hh ; (1) Ntotal Nvv + Nvh + Nhv + Nhh where Nvv is the number (or rate) of coincidences where both photons are vertically polarized, etc. E can range from -1, meaning that all photon coincidences have opposite polarizations, to 1, meaning they all have the same polarization. Let us then define the quantity, S, which is function of four distinct E measurements. S = E(α; β) − E(α; β0) + E(α0; β) + E(α0; β0) ; (2) 3 where α and β are the angles in which we are going to analyze the polarization of each photon. The interest of defining the quantity S is that localp realistic theories are always bound to yield jSj ≤ 2, while quantum mechanics allows values of up to 2 2 ≈ 2:8. At first glance, it would seem that S could range from 4 to 4. However, a careful inspection of the physics reveals that no two pairs of angles (α; α0) and (β; β0) give a value this large. If the system obeys a local hidden variable theory, then S is restricted by the CHSH inequality: jSj ≤ 2. However, quantum mechanics predicts that jSj can be as high as 22 for particular quantum states of the two photons and as well as carefully chosen angles. (For a full derivation, see CHSH's paper [3].) The goal of this experiment is to violate the CHSH inequality, thereby rejecting local hidden variable theories and affirming the validity of quantum mechanics. 6 Experimental Setup 6.1 Overview The heart of the experiment is the generation of a particular entangled quantum state of the polarization of two individual photons, a Bell state. In the simplest case, this is a superposition state of both photons being either horizontally or vertically polarized. In the experiment, we achieve this by sending photons near 405 nm from a diode laser to a pair of non-linear crystals made of beta barium borate (BBO crystal). Within the non-linear crystals the violet photon can decay into a pair of red photons with their polarization being determined by the optical axes of the non-linear crystals. The photon pair emitted under a small angle is then detected after passing through optics for manipulating polarization with two Avalanche Photodiodes (APD). (See the quadsupply diagram here) Finding the two detectors firing within a short time interval indicates that these events were indeed caused by a photon pair and not stray light. When you enter the room, you'll notice there are two boxes on the table. Each of these boxes houses different elements of the experiment. The one closer to the door (Box 1) holds the diode laser and optical elements for creating a Bell State. The one closer to the computer (Box 2) holds the detection setup. When aligning the laser it is best to take the top off both boxes and use the protective orange glasses when the laser is on. When taking data, you will want easy access to the half wave plates in the detector setup, so you can leave the top off of box 2. Ambient light will flood the detectors, so you will want the lights off in the room (computer light is ok). There is an LED lamp [8] (can you explain why we use blue LEDs? hint: you can look at the APD efficiency versus wavelength in the manual if you are interested.) installed so that you can read the values off of the half wave plates in the detector setup. The `on' switch for the lamp can be found on the back side of the table on the rack above. While taking data, it is ok not wearing the orange glasses as long as the top of Box 1 is in place. Inside Box 1, the diode laser has a maximum power of around 120 mW. At 405 nm, this can seriously damage your eye. However, in Box 2 the power is down to about 0.2 mW, which will not cause serious damage. You should use the power meter located in the room to confirm that the power of the laser beam in Box 2 is not too high. Record the number. If you find it high, ensure that the filter is in place on the BBOs. The filter should never be removed. Of course you should avoid looking directly into the beam. This setup makes collecting data more efficient.
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